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4.1 Introduction Determinants are special numbers associated with square matrices. They help in finding the inverse of a matrix, solving linear equations, and calculating the area of a triangle using…

3.1 Introduction Matrices are an important tool in mathematics used to arrange data in rows and columns. They are widely applied in science, engineering, economics, and computer graphics. In Class…

2.1 Introduction Trigonometric functions such as sin, cos, tan, cot, sec, and cosec are widely used in mathematics. However, these functions are not one-one over their complete domains, so their…

1.1 Introduction In mathematics, relations and functions help us understand how elements of one set are connected to elements of another set. These concepts are widely used in algebra, calculus,…

Class 12 Mathematics Notes Relations and Functions Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Applications of Derivatives Integrals Applications of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Linear…

Introduction to Graphs – Quick Notes (Class 8 ) 1. Definition: A graph is a visual representation of data. It shows the relationship between two variables. Variables: Quantities that can…

Factorization – Quick Notes Class 8 1. Definition: Factorization is the process of expressing an algebraic expression as a product of its factors. Example: x2+5x=x(x+5)x^2 + 5x = x(x +…

Direct and Inverse Proportions – Quick Notes (Class 8 NCERT) 1. Direct Proportion Definition: Two quantities are in direct proportion if one increases, the other increases, and one decreases, the…

Exponents and Powers – Quick Notes (Class 8 NCERT) 1. Definition: An exponent or power of a number tells how many times the number is multiplied by itself. Example: 23=2×2×2=82^3…

Mensuration – Quick Notes (Class 8 NCERT) Definition: Mensuration deals with measuring lengths, areas, and volumes of geometrical shapes and solids. Applications: Area of land, surface area of solids, volume…